APPENDICE B Modelli analitici per il calcolo del SIF

(1)

195

APPENDICE B

(2)

196

Modello empirico di Newman & Raju

K I φ

( )

(

S t H φ+

( )

⋅S b

)

π a⋅ Q ⋅ ⋅F

( )

φ := Q 1 1.464 a c









1.65 ⋅ + := F

( )

φ

( )

_{M 1} _{M 2} a t









2 ⋅ + _{M 3} a t









4 ⋅ +













⋅f

( )

φ ⋅g

( )

φ := M 1 1.13 0.09 a c









⋅ − := M 2 −0.54 0.89 0.2 a c









+ + := M 3 0.5 1 0.65 a c









+ − 14 1 a c −









24 ⋅ + := f

( )

φ a c









2 cos

( )

φ 2 ⋅ +sin

( )

φ 2













1 4 := g

( )

φ 1 0.1 0.35 a t









2 ⋅ +













(

1 sin−

( )

φ

)

2 ⋅ + := H

( )

φ := _{H 1}+

(

_{H 2 H 1}−

)

⋅sin

( )

φ p p 0.2 a c + 0.6 a t ⋅ + := H 1 1 0.34 a t ⋅ − 0.11 a c ⋅ a t









⋅ − := H 2 1 _{G 1} a t









⋅ + _{G 2} a t









2 ⋅ + := G 1 −1.22 0.12 a c ⋅ − := G 2 0.55 1.05 a c









0.75 ⋅ − 0.47 a c









1.5 ⋅ + :=

S

t ed

S

b sono rispettivamente la componente membranale e flessionale della tensione

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197

Modello alla “weight function” di T.Fett

K

( )

φ := _{K 0 φ}

( )

+_{K 1 φ}

( )

K 0 φ

( )

:= σ 0 π a⋅ ⋅ ⋅_{F 0 φ}

( )

F 0 φ

( )

M 1 f φ⋅

( )

⋅g

( )

φ 1+ 1.464⋅β1.65 := β a c := M 1 := 1.13 0.1− ⋅ _{β β 1}⋅ β 1 tanh β:=

( )

50 0.02 f

( )

φ



( )

β2 ⋅cos

( )

φ 2+ sin

( )

φ 2



1 4 := g

( )

φ := 1+ 0.1 1 sin⋅

(

−

( )

φ

)

2 K 1 φ

( )

:= σ 1 π a⋅ ⋅ ⋅_{F 1 φ}

( )

F 1 φ

( )

C 0 C 1 cos



1₂⋅π −φ







⋅ + +_{C 2 cos π 2 φ}⋅

(

− ⋅

)

:= z exp −3 2 ⋅β









:= C 0 := 0.787 z⋅ +0.6815 z⋅ 2 C 1 := 0.4647 0.0243− ⋅β −_{C 0} C 2 := 0.1762 0.0882− ⋅β −0.1524⋅β2 +0.0992⋅β3 −0.0133⋅β4−0.00128⋅β5

σ

0 e

σ

1 sono termini dello sviluppo lineare della distribuzione di tensione normale al